Sr Examen
Otras calculadoras
- Derivada de una función implícitamente dada
- Derivada de una función paramétrica
- Derivada parcial de la función
- Análisis de la función gráfica
- Integrales paso a paso
- Ecuaciones diferenciales paso a paso
- Límites paso por paso
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¿Cómo usar?
- Derivada de:
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Derivada de (x+12)e^(12-x)
- Derivada de u/v
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Derivada de t+1
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Derivada de (sqrt(x)-1)/(sqrt(x^2)-x-1)
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Expresiones idénticas
- y=(arccosx)^ln2^x
- y es igual a (arc coseno de x) en el grado ln2 en el grado x
- y=(arccosx)ln2x
- y=arccosxln2x
- y=arccosx^ln2^x
Derivada de y=(arccosx)^ln2^x
Solución
Ha introducido
[src]
x
log (2)
(acos(x))
$$\operatorname{acos}^{\log{\left(2 \right)}^{x}}{\left(x \right)}$$
acos(x)^(log(2)^x)
Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
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Simplificamos:
Respuesta:
Primera derivada
[src]
x / x \
log (2) | x log (2) |
(acos(x)) *|log (2)*log(acos(x))*log(log(2)) - -------------------|
| ________ |
| / 2 |
\ \/ 1 - x *acos(x)/
$$\left(\log{\left(2 \right)}^{x} \log{\left(\log{\left(2 \right)} \right)} \log{\left(\operatorname{acos}{\left(x \right)} \right)} - \frac{\log{\left(2 \right)}^{x}}{\sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}}\right) \operatorname{acos}^{\log{\left(2 \right)}^{x}}{\left(x \right)}$$
Segunda derivada
[src]
x / 2 \
log (2) x | 1 / 1 \ x 2 x 2*log(log(2)) |
(acos(x)) *log (2)*|------------------ + |log(acos(x))*log(log(2)) - -------------------| *log (2) + log (log(2))*log(acos(x)) - ------------------- - -------------------|
|/ 2\ 2 | ________ | 3/2 ________ |
|\-1 + x /*acos (x) | / 2 | / 2\ / 2 |
\ \ \/ 1 - x *acos(x)/ \1 - x / *acos(x) \/ 1 - x *acos(x)/
$$\left(- \frac{x}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{acos}{\left(x \right)}} + \left(\log{\left(\log{\left(2 \right)} \right)} \log{\left(\operatorname{acos}{\left(x \right)} \right)} - \frac{1}{\sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}}\right)^{2} \log{\left(2 \right)}^{x} + \log{\left(\log{\left(2 \right)} \right)}^{2} \log{\left(\operatorname{acos}{\left(x \right)} \right)} + \frac{1}{\left(x^{2} - 1\right) \operatorname{acos}^{2}{\left(x \right)}} - \frac{2 \log{\left(\log{\left(2 \right)} \right)}}{\sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}}\right) \log{\left(2 \right)}^{x} \operatorname{acos}^{\log{\left(2 \right)}^{x}}{\left(x \right)}$$
Tercera derivada
[src]
x / 3 2 2 \
log (2) x |/ 1 \ 2*x 3 1 2 3*x 3*x 3*log (log(2)) x / 1 \ / 1 2 x 2*log(log(2)) \ 3*log(log(2)) 3*x*log(log(2)) |
(acos(x)) *log (2)*||log(acos(x))*log(log(2)) - -------------------| *log (2) + log (log(2))*log(acos(x)) - ------------------- - -------------------- - ------------------- - ------------------- - ------------------- - 3*log (2)*|log(acos(x))*log(log(2)) - -------------------|*|- ------------------ - log (log(2))*log(acos(x)) + ------------------- + -------------------| + ------------------ - -------------------|
|| ________ | 3/2 3/2 2 5/2 ________ | ________ | | / 2\ 2 3/2 ________ | / 2\ 2 3/2 |
|| / 2 | / 2\ / 2\ 3 / 2\ 2 / 2\ / 2 | / 2 | | \-1 + x /*acos (x) / 2\ / 2 | \-1 + x /*acos (x) / 2\ |
\\ \/ 1 - x *acos(x)/ \1 - x / *acos(x) \1 - x / *acos (x) \-1 + x / *acos (x) \1 - x / *acos(x) \/ 1 - x *acos(x) \ \/ 1 - x *acos(x)/ \ \1 - x / *acos(x) \/ 1 - x *acos(x)/ \1 - x / *acos(x)/
$$\left(- \frac{3 x^{2}}{\left(1 - x^{2}\right)^{\frac{5}{2}} \operatorname{acos}{\left(x \right)}} - \frac{3 x}{\left(x^{2} - 1\right)^{2} \operatorname{acos}^{2}{\left(x \right)}} - \frac{3 x \log{\left(\log{\left(2 \right)} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{acos}{\left(x \right)}} + \left(\log{\left(\log{\left(2 \right)} \right)} \log{\left(\operatorname{acos}{\left(x \right)} \right)} - \frac{1}{\sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}}\right)^{3} \log{\left(2 \right)}^{2 x} - 3 \left(\log{\left(\log{\left(2 \right)} \right)} \log{\left(\operatorname{acos}{\left(x \right)} \right)} - \frac{1}{\sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}}\right) \left(\frac{x}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{acos}{\left(x \right)}} - \log{\left(\log{\left(2 \right)} \right)}^{2} \log{\left(\operatorname{acos}{\left(x \right)} \right)} - \frac{1}{\left(x^{2} - 1\right) \operatorname{acos}^{2}{\left(x \right)}} + \frac{2 \log{\left(\log{\left(2 \right)} \right)}}{\sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}}\right) \log{\left(2 \right)}^{x} + \log{\left(\log{\left(2 \right)} \right)}^{3} \log{\left(\operatorname{acos}{\left(x \right)} \right)} + \frac{3 \log{\left(\log{\left(2 \right)} \right)}}{\left(x^{2} - 1\right) \operatorname{acos}^{2}{\left(x \right)}} - \frac{3 \log{\left(\log{\left(2 \right)} \right)}^{2}}{\sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}} - \frac{1}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{acos}{\left(x \right)}} - \frac{2}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{acos}^{3}{\left(x \right)}}\right) \log{\left(2 \right)}^{x} \operatorname{acos}^{\log{\left(2 \right)}^{x}}{\left(x \right)}$$
Gráfico